Browsing by Author "Bessaih, Hakima"

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    Space-Time Euler Discretization Schemes for the Stochastic 2D Navier-Stokes Equations
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2020) Bessaih, Hakima; Millet, Annie
    We prove that the implicit time Euler scheme coupled with finite elements space discretization for the 2D Navier-Stokes equations on the torus subject to a random perturbation converges in L²(Ω), and describe the rate of convergence for an H¹-valued initial condition. This refines previous results which only established the convergence in probability of these numerical approximations. Using exponential moment estimates of the solution of the stochastic Navier-Stokes equations and convergence of a localized scheme, we can prove strong convergence of this space-time approximation. The speed of the L²(Ω)-convergence depends on the diffusion coefficient and on the viscosity parameter. In case of Scott-Vogelius mixed elements and for an additive noise, the convergence is polynomial.